Quantitative Aptitude Ques 25

Question: If $ x+\frac{1}{x}=9, $ $ (x\ne 0), $ then the value of $ \frac{x^{2}-4x+1}{x^{2}+6x+1} $ is

Options:

A) $ \frac{1}{3} $

B) $ \frac{2}{3} $

C) 3

D) 4

Show Answer

Answer:

Correct Answer: A

Solution:

  • $ \frac{x^{2}-4x+1}{x^{2}+6x+1}=\frac{x-4+\frac{1}{x}}{x+6+\frac{1}{x}}=\frac{x+\frac{1}{x}-4}{x+\frac{1}{x}+6} $ $ =\frac{9-4}{9+6}=\frac{5}{15}=\frac{1}{3} $